2.2. Cox Regression

Concept

Cox regression, also known as proportional hazard regression, is a method to investigate the effect of one or multiple factors (i.e. gene expressions) upon the time an event of interest occurs. In this model, the effect of a unit increase in a factor is multiplicative with respect to the hazard rate.

Usage

A Cox regression analysis can be conducted by applying the following steps:

1. Select the analysis method as Cox Regression from Analysis tab.
2. Select suitable variables for the analysis, such as survival time, status variable, category value for status variable, and categorical and continuous predictors for the model.
3. In advanced options, interaction terms, strata terms and time dependent covariates can be added to the model. Moreover, if there are multiple records for observations, users can specify it by clicking Multiple ID checkbox. Furthermore, once can choose model selection criteria, as AIC or p-value, model selection method, as backward, forward or stepwise, reference category, as first or last, and ties method, as Efron, Breslow or exact and change the confidence level.
   
4. Click Run button to run the analysis.

Outputs

Desired outputs can be selected by clicking Outputs checkbox. Available outputs are coefficient estimates, hazard ratio, goodness of fit tests, analysis of deviance, predictions, residuals, Martingale residuals, Schoenfeld residuals and DfBetas.

a. Coefficient Estimates

A coefficient estimation table, which includes variable names, coefficient estimates and their associated standard errors, z statistics and p values, can be created.

b. Hazard ratio

A hazard ratio table, which includes variable names, hazard ratios and their associated lower and upper limits, can be created.

c. Hazard plot

A forest plot can be created for hazard ratios to give them a visual inpection.

d. Goodness of Fit Tests

Fitted Cox regression model can be tested with three tests: Likelihood ratio, Wald, Score.

e. Analysis of Deviance

A deviance analysis can be conducted for each variable in the fitted model.

f. Predictions

Predictions from the fitted model can be obtained.

g. Residuals

Residuals from the fitted model can be obtained.

h. Martingale Residuals

Martingale residuals from the fitted model can be obtained.

i. Schoenfeld Residuals

Schoenfeld residuals from the fitted model can be obtained.

j. DfBetas

DfBetas residuals from the fitted model can be obtained.

k. Proportional Hazard Assumption

l. Proportional Hazard Test

To check the proportionality assumption of Cox regression model, a proportional hazard test can be conducted both globally and for each variable in the fitted model.

m. Schoenfeld Plot

Beside a formal test for proportionality assumption, a Schoenfeld plot can be created to check the assumption visually.

n. Log-Minus-Log Plot

Another useful plot for checking proportionality assumption is log-minus-log plot. Lines should be parallel to each other to satisfy proportionality.